1. No such thing as a “spirit”. 2. Multiverse. You do not emerge in the past of your own time line, but an alternate one. You kill an alternate past self, not your own. 2b. Causal disconnect. The very act of time travel might disconnect you from the chain of cause and effect. So even if you kill your own past self, you will not be affected. 3. Another valid possibility. Any action you take in the past was already part of the timeline that you left. In this specific case, not only will you not succeed in killing your past self, since you are in fact, still alive, but you will not even meet your past self, since you did not meet your future self in the past.